The heater core could cause your car to overheat if the heater core is leaking or you have other coolant leaks such as heater hoses, radiator hoses etc leaking.
If your heater core is leaking then yes it could be a cause of your vehicle to overheat but I would also check other parts of the cooling system on your car such as the radiator, water pump, thermostat housing, head gasket, freeze plugs etc.
Those are all things that could be leaking besides your heater core that could cause a cars engine to overheat.